Molecular Orbital Theory for Diatomics: Bond Order and Magnetism
MO diagrams answer three questions at once — is the molecule stable, how strong is the bond, and is it paramagnetic.
The core idea
When two atomic orbitals of comparable energy and correct symmetry overlap, they combine to give two molecular orbitals: one bonding, lower in energy than either parent, and one antibonding, higher. Electrons in bonding orbitals hold the molecule together; electrons in antibonding orbitals push it apart.
A bond order of zero means the molecule does not exist as a stable species, which is the standard explanation for why the helium molecule is not observed.
Filling order, and the s–p mixing complication
For second-period diatomics the ordering depends on whether s–p mixing is significant:
| Elements | Ordering | Reason |
|---|---|---|
| Li through N | π(2p) below σ(2p) | 2s and 2p are close in energy, so mixing raises σ(2p) |
| O, F, Ne | σ(2p) below π(2p) | The 2s–2p gap is large, so mixing is negligible |
The classic results
| Species | Valence electrons | Bond order | Magnetism |
|---|---|---|---|
| H2 | 2 | 1 | Diamagnetic |
| He2 | 4 | 0 | Does not exist |
| N2 | 10 | 3 | Diamagnetic |
| O2 | 12 | 2 | Paramagnetic — two unpaired electrons |
| F2 | 14 | 1 | Diamagnetic |
Oxygen is the reason MO theory is taught at all. Valence bond theory draws a double bond with all electrons paired and predicts diamagnetism. Oxygen is experimentally paramagnetic. MO theory places the last two electrons singly in two degenerate π* orbitals, predicting exactly two unpaired electrons. This single case is the standard argument for MO theory and appears in almost every syllabus.
Ions, and what removing an electron does
Adding or removing electrons changes bond order predictably. Removing a bonding electron lowers bond order and lengthens the bond; removing an antibonding electron raises bond order and shortens it.
So O2+ has a higher bond order than O2, because the electron removed came from an antibonding orbital, while O2− and O22− have progressively lower bond orders. Ordering a set of oxygen species by bond length is a routine question, and it is answered entirely by counting antibonding electrons.
Heteronuclear diatomics
When the two atoms differ, their atomic orbitals sit at different energies. The more electronegative atom's orbitals lie lower, so the bonding MO resembles them more closely and the antibonding MO resembles the less electronegative atom's. This unequal contribution is the MO description of bond polarity.
Carbon monoxide is the standard case. Its highest occupied orbital is concentrated on carbon, which is why CO binds to metals through carbon rather than oxygen — a fact usually memorised and rarely explained, and worth being able to justify.
Frequently asked questions
Why do only orbitals of similar energy combine?
Because the stabilisation from mixing falls as the energy gap widens. Orbitals far apart in energy interact negligibly, which is why core orbitals are ignored in these diagrams.
What decides whether overlap is allowed at all?
Symmetry. Orbitals must have matching symmetry with respect to the internuclear axis; if they do not, the positive and negative overlap regions cancel exactly and no bond results.
Does a higher bond order always mean a shorter bond?
Within a series of related species, yes. Comparing across different elements it does not hold reliably, since atomic size changes too.
How does s–p mixing actually change the ordering?
Mixing pushes the σ(2s) down and the σ(2p) up. Where mixing is strong, σ(2p) rises above the π(2p) pair, reversing the expected order.
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